Peng Linqing, Zhang Xing, Chan Garnet Kin-Lic
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States.
J Chem Theory Comput. 2023 Dec 26;19(24):9151-9160. doi: 10.1021/acs.jctc.3c00851. Epub 2023 Dec 14.
Fermionic reduced density matrices summarize the key observables in Fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest. Here, we consider the possibility of using matrix completion to reconstruct the two-particle reduced density matrix to chemical accuracy from partial information. We consider the case of noiseless matrix completion, where the partial information corresponds to a subset of the 2-RDM elements, as well as noisy completion, where the partial information corresponds to both a subset of elements and statistical noise in their values. Through experiments on a set of 24 molecular systems, we find that 2-RDM can be efficiently reconstructed from a reduced amount of information. In the case of noisy completion, this results in a multiple orders of magnitude reduction in the number of measurements needed to determine the 2-RDM with chemical accuracy. These techniques can be readily applied to both classical and quantum algorithms for quantum simulations.
费米子约化密度矩阵总结了费米子系统中的关键可观测量。在电子系统中，两体约化密度矩阵（2-RDM）足以确定能量以及大多数感兴趣的物理可观测量。在此，我们考虑利用矩阵补全从部分信息中以化学精度重构两体约化密度矩阵的可能性。我们考虑无噪声矩阵补全的情况，其中部分信息对应于2-RDM元素的一个子集，以及有噪声补全的情况，其中部分信息既对应于元素的一个子集，又对应于其值中的统计噪声。通过对一组24个分子系统进行实验，我们发现可以从减少的信息量中高效地重构2-RDM。在有噪声补全的情况下，这使得以化学精度确定2-RDM所需的测量次数减少了多个数量级。这些技术可以很容易地应用于量子模拟的经典算法和量子算法。
